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arXiv · 1501.02994

$q$-Borel-Laplace summation for $q$-difference equations with two slopes

Thomas Dreyfus·Anton Eloy
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Abstract

In this paper, we consider linear $q$-difference systems with coefficients that are germs of meromorphic functions, with Newton polygon that has two slopes. Then, we explain how to compute similar meromorphic gauge transformations than those appearing in the work of Bugeaud, using a $q$-analogue of the Borel-Laplace summation.

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Thomas Dreyfus, Anton Eloy. 2016-06-25. $q$-Borel-Laplace summation for $q$-difference equations with two slopes. https://doi.org/10.1080/10236198.2016.1209192

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